System and method for expanding a set of random values

ABSTRACT

A system and method for producing an expanded set of random values is provided. An initial random value input set is separated into a first group, a second group, and a third group. A first value from the first group, a second value from the second group, and a third value from the third group are retrieved. A mathematical operation associated with the third value is retrieved from a set of mathematical operations. The retrieved mathematical operation is applied to the first value and the second value to arrive at a first new random value.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application Ser.No. 62/636,484 filed Feb. 28, 2018, the disclosures of which are herebyincorporated by reference as if fully restated herein.

TECHNICAL FIELD

Exemplary embodiments relate generally to a system and method forexpanding a set of random values.

BACKGROUND AND BRIEF SUMMARY OF THE INVENTION

Random numbers are useful for many applications including scientifictesting, statistics, art, cryptography, gaming, and gambling, to name afew examples. Random numbers may be used for purposes of scientificanalysis to simulate the tosses of a coin, the rolling of a die, theoccurrences of automobile accidents, the births and deaths ofindividuals in a population, and whatever physical phenomenon is capableof a statistic description. From a calculation point of view, randomnumbers may be used to randomize experiments in the laboratory(eliminating observational bias), to ensure random sampling instatistical surveys (in population studies, census taking, forecasting,and the like), to provide the randomizing element in any industrialquality control procedure, for security encryption, and to aid in theperformance of many other mathematical tasks, just to name a fewpossible applications.

Pseudo random number generators are algorithms which may be used tosimulate randomness. While effective in some applications, pseudo randomnumber generators do possess some level of predictability. The closerone can get to simulating or recreating true randomness, the moreeffective the random number generation is.

In some applications, a set or block of random numbers may be required.An exemplary application for a block of random numbers is cryptography,where the block of random numbers may be used as the basis for encodinga block of data. Again, the closer one can get to simulating orrecreating true randomness, the more effective the cryptography, andtherefore security, will be. As those of skill in the arts willrecognize, this is just one exemplary application.

A block or set of random numbers can be produced through, for examplewithout limitation, the use of two large groups: first, a groupcomprised of measuring devices whereby irregular patterns of naturalphenomena may be measured and recorded in the form of numbers; andsecond, a group comprised of computing machines whereby the measurementof erratic behavior can be transformed into numbers. Exemplary objectsof measurement for the first group are phenomena such as thermal motionof electrons in a resistor, variation in electron emission from a heatedcathode, Brownian motion of microscopic particles suspended in a fluid,arrival times of cosmic rays, outcomes in games of chance, and the like.Devices have been designed expressly to measure such natural phenomenasuch as electrical amplifiers, microscopes, Geiger counters, and otherelectromechanical devices. Computing machines of the second group ofdevices have been designed to measure erratic behavior in theinteraction and interfacing between solid state computing and physicaland electrical operations of devices and networks.

While these two large groups of devices may be configured to produce ablock or set of random numbers, the time necessary to transform theseobservations into usable numbers may be a limiting factor for use. Sincethe creation of truly random numbers depends upon the observation ofrandom events, there are inherent timing factors which may directlyaffect the creation of a set of random numbers. Therefore, theusefulness of such a set of truly random numbers may be limited due tothe time necessary for its creation. Use of a purely mathematicalformula to create a larger set of random numbers would be biased by itsown regulated application. As such, a faster system and method forproducing a larger set or block of random numbers is needed.Furthermore, this system and method must utilize the smaller set ofrandom numbers in a way that will extend the randomness of the initialset while increasing the size of the set to something usable. Therefore,what is needed is a system and method for expanding a set of randomvalues.

A system and method for expanding a set of random values is provided.This disclosure provides a system and method where a manipulativeprocess may be applied against one or more sets of random numbers inorder to produce a larger set of random numbers that maintains therandom character of the smaller, initial inputs. By dividing theoriginal set of numbers into three or more sets of random numbers andapplying a random series of mathematical operations between them, theoriginal randomness will be reflected in the resulting larger set. Inthis way, a significantly larger set of random numbers may be produced.This larger set of random numbers may allow for greater use from theoriginal, smaller set of random inputs without the need to wait for theobservation of additional random events. The three or more sets ofrandom numbers may be random in size. Values other than numbers may beused in exemplary embodiments.

Further features and advantages of the systems and methods disclosedherein, as well as the structure and operation of various aspects of thepresent disclosure, are described in detail below with reference to theaccompanying figures.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

Novel features and advantages of the present invention, in addition tothose mentioned above, will become apparent to those skilled in the artfrom a reading of the following detailed description in conjunction withthe accompanying drawings wherein identical reference characters referto identical parts and in which:

FIG. 1 is a simplified diagram depicting an exemplary expansion of a setof random numbers into a larger, usable set of random numbers; and

FIG. 2 is a flow chart illustrating exemplary logic.

DETAILED DESCRIPTION OF THE INVENTION

Various embodiments of the present invention will now be described indetail with reference to the accompanying drawings. In the followingdescription, specific details such as detailed configuration andcomponents are merely provided to assist the overall understanding ofthese embodiments of the present invention. Therefore, it should beapparent to those skilled in the art that various changes andmodifications of the embodiments described herein can be made withoutdeparting from the scope and spirit of the present invention. Inaddition, descriptions of well-known functions and constructions areomitted for clarity and conciseness.

Embodiments of the invention are described herein with reference toillustrations of idealized embodiments (and intermediate structures) ofthe invention. As such, variations from the shapes of the illustrationsas a result, for example, of manufacturing techniques and/or tolerances,are to be expected. Thus, embodiments of the invention should not beconstrued as limited to the particular shapes of regions illustratedherein but are to include deviations in shapes that result, for example,from manufacturing.

Referring to FIG. 1, a set of random numbers 110 may be divided 112 intothree or more sets: set A 114, set B 116, and set C 118, for examplewithout limitation. Each set 114, 116, and 118 may be of a varying size.In exemplary embodiments, the size of the sets 114, 116, and 118 isitself random. Each set 114, 116, and 118 may be of the same, or of adifferent, size. Set A 114 and set B 116 may be used as operands, orelements, to be expanded. In exemplary embodiments, the initial set ofnumbers 110 may be comprised of truly random numbers.

The system and method may include a series of mathematical operations(hereinafter also “the mechanic” 122) which may be applied to elementsfrom sets A 114 and B 116. The numbers in set C 118 may be used toselect the mechanic 122 for application with values from set A 114 andset B 116. In other words, set C 118 may be the set of random numbersthat provides the random values to be used to select a mechanic 122 foruse on the values from set A 114 and set B 116, herein the value fromset C 118 is also termed “Q”. Set D 120 may be the expanded set ofrandom numbers produced through the application of the mechanic 122,selected using set C 118, and applied to the random numbers from set A114 and B 116. In exemplary embodiments where more than three sets 114,116, and 118 are utilized, the mechanic 122 may be applied to valuesfrom any number of sets 114, 116, and 118. Furthermore, while theprovided example selects the mechanic 122 based on the value from set C118, it is contemplated that the value for the mechanic 122 may comefrom any of the sets 114, 116, and 118.

The set C 118 may be used to select the mechanic 122 operation that willbe used to perform a transformation on elements in set A 114 and set B116 to produce one element for set D 120. In exemplary embodiments, setA 114 and set B 116 may be placed into a nested loop and be continuallyused until the desired number of elements in set D 120 are produced,which may be the desired random number of elements in set D 120. Set C118 may be continually looped for the selection of the mechanic 122. Inexemplary embodiments where set A 114 and set B 116 are in a nestedloop, and set C 118 is in a conventional loop, set D 120 will never havethe same two elements from set A 114 and set B 116. Furthermore, set D120 will never have the same mechanic 122 from set C 118 applied.

The term “Mechanic” 122 is used herein to denote the operand oroperations that may be applied against elements from set A 114 and set B116. The following are examples of mechanics 122, where a_(r) and b_(s)represent elements from set A 114 and set B 116:

-   -   [1] a_(r)×b_(s)    -   [2] a_(r)+b_(s)    -   [3] a_(r)−b_(s)    -   [4] b_(s)−a_(r)    -   . . . .    -   etc.

The above mechanics 122, as those of skill in the art will recognize,are merely exemplary and are not intended to be limiting. Anymathematical operation is contemplated, such as but not limited to,addition, subtraction, multiplication, division, some combinationthereof, or the like. For example, in embodiments where more than threesets 112, 114, or 116 are used, the mechanics 112 may likewise beexpanded to utilize all remaining sets 112, 114, or 116. Each operationwithin the set of possible mechanics 122 may be simple in nature, inexemplary embodiments without limitation, and applied against only oneelement from set A 114 and set B 116. The absolute value of theresulting number may be taken. Each additional element added to set D120 may further iterate the random data such that more random numbersmay be obtained from a smaller amount of quantified random observations.The mechanics 122 may be predetermined and stored in a local or remoteelectronic storage device.

FIG. 2 is a flow chart illustrating exemplary logic. An initial set ofrandom numbers 110 may be generated and subdivided into at least threesubsets 114, 116, and 118. These subsets 114, 116, and 118 may be ofrandom size(s). For convenience, these subsets may be referred to hereinas set A 114, set B 116, and set C 118. A value may be retrieved fromeach set 114, 116, and 118. In exemplary embodiments, numbers may beretrieved sequentially. The value pulled from set C 118 may be used todetermine a mathematical operation(s) to be performed on the values fromset A 114 and set B 116. However, in other embodiments, the value usedto determine the mathematical operation(s) to be performed may be pulledfrom either set A 114 or set B 116 and the values from the remainingsets 112, 114, or 116 may be operated on.

In exemplary embodiments, a number of predetermined mathematicaloperations are stored in a connected electronic storage device and eachoperation is associated with a given value. The determined mathematicaloperation may be performed against the values from the remaining sets112, 114, or 116 to generate a first value for a new set 120, which forconvenience is referred to herein as set D 120. The mathematicaloperation performed may comprise addition, subtraction, multiplication,division, some combination thereof, or the like. The absolute value ofthe resulting number may be taken. Subsequent values may be pulled fromthe subsets 114, 116, and 118 and the process may be repeated.

In some exemplary embodiments, the subsets 114, 116, and 118 may becombined with the new set D 120 in order to create an expanded set ofrandom numbers.

Certain operations described herein may be performed by one or moreelectronic devices. Each electronic device may comprise one or moreprocessors, electronic storage devices, executable softwareinstructions, and the like configured to perform the operationsdescribed herein. The electronic devices may be general purpose orspecialized computing devices. The electronic devices may be personalcomputers, smartphone, tablets, databases, servers, or the like.

While several exemplary embodiments are described herein with respect tonumbers, those of skill in the arts will recognize that in otherexemplary embodiments any type of value may be utilized.

Any embodiment of the present invention may include any of the optionalor exemplary features of the other embodiments of the present invention.The exemplary embodiments herein disclosed are not intended to beexhaustive or to unnecessarily limit the scope of the invention. Theexemplary embodiments were chosen and described in order to explain theprinciples of the present invention so that others skilled in the artmay practice the invention. Having shown and described exemplaryembodiments of the present invention, those skilled in the art willrealize that many variations and modifications may be made to thedescribed invention. Many of those variations and modifications willprovide the same result and fall within the spirit of the claimedinvention. It is the intention, therefore, to limit the invention onlyas indicated by the scope of the claims.

What is claimed is:
 1. A method for producing an expanded set of randomvalues comprising the steps of: obtaining an initial random value inputset; separating the initial random value input set into a first group, asecond group, and a third group; retrieving a first value from the firstgroup, a second value from the second group, and a third value from thethird group; retrieving a mathematical operation associated with thethird value from a set of mathematical operations; and applying theretrieved mathematical operation to the first value and the second valueto arrive at a first new random value.
 2. The method of claim 1 furthercomprising the steps of: retrieving a fourth value from the first group,a fifth value from the second group, and a sixth value from the thirdgroup; retrieving a second mathematical operation associated with thesixth value; and applying the retrieved mathematical operation to thefourth value and the fifth value to arrive at a second new random value.3. The method of claim 1 wherein: the steps of retrieving values fromthe first, second, and third groups, retrieving a mathematical operationassociated with the value retrieved from the third group, and applyingthe retrieved mathematical operation to the values retrieved from thefirst and second groups is repeated until a new set of random values ofa predetermined size is generated.
 4. The method of claim 3 furthercomprising the steps of: combining the first group, the second group,the third group, and the new set of random values.
 5. The method ofclaim 1 wherein: the first group, the second group, and the third groupare random in size.
 6. The method of claim 5 wherein: the first group,the second group, and the third group are of different sizes.
 7. Themethod of claim 5 wherein: the first group, the second group, and thethird group are of equal size.
 8. The method of claim 1 wherein: the setof mathematical operations each comprise an operation selected from thegroup consisting of: addition, subtraction, multiplication, anddivision.
 9. The method of claim 8 further comprising the steps of:taking the absolute value of the first new random value.
 10. The methodof claim 1 wherein: the step of applying the retrieved mathematicaloperation to the first value and the second value comprises adding orsubtracting the first value to the second value.
 11. The method of claim1 wherein: the step of applying the retrieved mathematical operation tothe first value and the second value comprises multiplying or dividingthe first value by the second value.
 12. The method of claim 1 wherein:the initial random value input set consists of numbers.
 13. The methodof claim 1 wherein: the initial random value input set is derived fromobservance of random events occurring in nature.
 14. The method of claim13 wherein: the observed natural event is selected from the groupconsisting of: thermal motion of electrons in a resistor, variation inelectron emission from a heated cathode, Brownian motion of microscopicparticles suspended in a fluid, arrival times of cosmic rays, outcomesin games of chance.
 15. The method of claim 1 wherein: the initialrandom value input set is derived from observance of random eventsbetween networked computer systems.
 16. A method for producing anexpanded set of random numbers from an initial set of random numbers,said method comprising the steps of: (a) separating the initial set ofrandom numbers into at least a first subset, a second subset, and athird subset; (b) retrieving a number from the first subset (“numberA”), a number from the second subset (“number B”), and a number from thethird subset (number “C”); (c) retrieving a mathematical operationassociated with a value matching the number C from a plurality ofmathematical operations; (d) performing the retrieved mathematicaloperation on number A and number B to arrive at a new random number; and(e) repeating steps (b)-(d) until a predetermined number of new randomnumbers are generated to arrive at a new set of random numbers.
 17. Themethod of claim 16 wherein: said plurality of mathematical operationscomprises adding number A to number B, subtracting number A from numberB, multiplying number A from number B, and dividing number A by numberB.
 18. The method of claim 17 further comprising the steps of: takingthe absolute value of the new random number.
 19. The method of claim of16 further comprising the steps of: combining the first subset, thesecond subset, the third subset, and the new set of random numbers. 20.A method for producing an expanded set of random numbers comprising thesteps of: (a) providing a plurality of mathematical operations, whereineach mathematical operation is a function of two variables and isassociated with a value; (b) generating an initial set of random numbersderived from observance of erratic behaviors in nature or in electronicsystems; (c) separating the initial set of random numbers into a firstgroup, a second group, and a third group, wherein the first group, thesecond group, and the third group are each of a random size; (d)retrieving a number from the first group (“number A”), a number from thesecond group (“number B”), and a number from the third group (number“C”); (e) retrieving the mathematical operation associated with a valuematching the number C from the plurality of mathematical operations; (f)performing the retrieved mathematical operation on number A and number Bto arrive at a new random number; (g) taking the absolute value of thenew random number to arrive at an absolute new random number; and (h)repeating steps (d)-(g) until a predetermined number of absolute newrandom numbers are generated.